There isn't really much that outright bothers me, but there are a few things that could have been done differently without calling it an outright design flaw.
1) The one exception to this and what I find to be a design flaw is the Ranger and Hunter's Mark. Hunter's Mark should be a Ranger-only ability, and it should neither require a bonus action to apply, a bonus action to transfer, nor require concentration to maintain. The Vengeance Paladin's Vow of Enmity exactly fits what Hunter's Mark should look like. And given that WotC explicitly stated concerning Clerics that they wanted their subclass features to play nice with the base class, they already knew about the issue and should just have transferred that idea to the Ranger.
2) Divine Smite does not need to be a spell. It could have remained a class ability. If the idea was to limit it to one use per round, this could have been achieved by simply adding the respective wording "once per turn". They managed to do just that with Eldritch Smite and I don't really see a reason why the two had to be mechanically different. If the intention here was that multiclassing characters could stack the two, Divine Smite also didn't need to be a spell.
3) Not a design flaw per se, but something that begins to bother me. Some people struggle with the wording of features, abilities, spells, and other aspects of the game and at times, something in the early chapters of the book needs to be read alongside something in the rules glossary to understand what the rules are for a particular situation. There's already the term "rules lawyering", but when you design the rules like this, it makes it appear like you want people to at least take a pre-law course at the local community college to be better equipped. I went to law school and in some situations, reading the rules feels not all that different from reading the General Terms and Conditions of a legal contract. And if you know even just the majority of the rules, some would regard you as a veteran. On top of that, people argue over RAW and some really dig their heels in to a point that reminds of fanaticism and zealotry. I think, instead of having all these specific rules, it would have been better to have fewer general rules and to allow the individual tables to make these determinations, especially when they even explicitly said that the rules are more intended to be a framework. But I guess, given that people regarded Jeremy Crawford's rulings as official, despite their inconsistencies, and then again unofficial after the release of SAC, people might have a desire for definitive rules. But even when it comes to simple things, the seemingly ever expanding number of rules can cause issues.
- For example, ranged attacks against targets within 5 feet have disadvantage unless the target is incapacitated, so then you need to flip through the book to see what causes the target to be incapacitated. Stunned and paralyzed targets, for example, but was it really necessary that those two are different conditions? They both cause the Incapacitated condition, they both cause the target to fail strength and dex saves, and they both give attack rolls against the target advantage. The only difference is that the Paralyzed condition also reduces the creatures speed to 0, and attacks from 5 feet are autocrits. With a 60% overlap, I'm really wondering whether that was necessary.
- Speaking of 5 feet, the prone condition can create similar strange situations. Why did it have to be "within 5 feet" rather than "melee attacks"? So, a Bugbear using his long arms or a creature using a reach weapon and attacking from 10 feet away has disadvantage? Why? Similarly, a Barbarian Berserker's Retaliation feature has a 5 feet range, so Bugbear Berserker or a Berserker using a Polearm can't use it even if the target is within their 10 feet melee range. Why?
- If I compare these rules to other areas, for example the change to Polearm Master that no longer views the Reactive Strike as an Opportunity Attack to prevent Forcelance builds, there is no or very little mechanical reason here to make this as convoluted or restrictive as it is.
4) From a more holistic point of view, in some cases, it feels like classes are not distinct enough. In some cases, it even feels like that some classes could have just been subclasses to other classes. That applies to both martials and spellcasters. There are several ways how this could be approached differently. Wizards and Sorcerers have much overlap with regards to their respective spell lists. Sorcerers and Warlocks share a lot of the same underlying concepts like the Great Old One Warlock and the Aberrant Mind Sorcerer. Sorcerers and Bards are both Charisma-based casters like Druids and Clerics are both Wisdom-based casters. Maybe not from a mechanical perspective, but from an RP-perspective - or what some call "class silhouette" - if there is struggle to make classes clearly distinct from one another, maybe they shouldn't be separate classes. Now, in some cases, I can see how it works with what we have. Druids and Clerics, for example, are both Wisdom-based casters, but they have vastly different spell lists and while one has Channel Divinity, the other has Wildshape. But we could have approached this from the angle of Nature Caster vs Divine Caster as a choice in the class progression, providing Wildshape and access to specific nature spells with one choice and providing Channel Divinity and specific divine spells with the other. Where that would be better, worse, or the same is for everyone themselves to decide.